High order hamiltonian approach to nonlinear oscillators

S. Durmaz; S. Altay Demirbaǧ; M. O. Kaya

doi:10.1515/IJNSNS.2010.11.8.565

High order hamiltonian approach to nonlinear oscillators

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

Abstract

This paper suggests a high order Hamiltonian approach to nonlinear oscillators. Two examples are given to illustrate the effectiveness of the method. The maximum relative error of Duffing oscillator obtained by He's Hamiltonian approach is 2.22% ; while the present approach leads to 0.19% and 0.009% accuracy, respectively, for the second and third approximations.

Original language	English
Pages (from-to)	565-570
Number of pages	6
Journal	International Journal of Nonlinear Sciences and Numerical Simulation
Volume	11
Issue number	8
DOIs	https://doi.org/10.1515/IJNSNS.2010.11.8.565
Publication status	Published - Aug 2010

Keywords

Duffing equation
Hamiltonian
High order hamiltonian approach
Nonlinear oscillator
Nonlinear oscillator with discontinuity

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10.1515/IJNSNS.2010.11.8.565

Cite this

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abstract = "This paper suggests a high order Hamiltonian approach to nonlinear oscillators. Two examples are given to illustrate the effectiveness of the method. The maximum relative error of Duffing oscillator obtained by He's Hamiltonian approach is 2.22\% ; while the present approach leads to 0.19\% and 0.009\% accuracy, respectively, for the second and third approximations.",

keywords = "Duffing equation, Hamiltonian, High order hamiltonian approach, Nonlinear oscillator, Nonlinear oscillator with discontinuity",

author = "S. Durmaz and \{Altay Demirbaǧ\}, S. and Kaya, \{M. O.\}",

year = "2010",

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AU - Kaya, M. O.

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AB - This paper suggests a high order Hamiltonian approach to nonlinear oscillators. Two examples are given to illustrate the effectiveness of the method. The maximum relative error of Duffing oscillator obtained by He's Hamiltonian approach is 2.22% ; while the present approach leads to 0.19% and 0.009% accuracy, respectively, for the second and third approximations.

KW - Duffing equation

KW - Hamiltonian

KW - High order hamiltonian approach

KW - Nonlinear oscillator

KW - Nonlinear oscillator with discontinuity

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JO - International Journal of Nonlinear Sciences and Numerical Simulation

JF - International Journal of Nonlinear Sciences and Numerical Simulation

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ER -

High order hamiltonian approach to nonlinear oscillators

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Keywords

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